The directionality of cellular appendages such as hairs and cilia in an epithelial sheet is established by the planar cell polarity (PCP) signaling pathway. In the fly wing epithelium, global positional signals transduced by the cadherin Fat orient cells with respect to the proximal-distal axis of the wing. Locally, however, polarization is propagated between neighboring cells by a feedback loop comprising the core PCP components Frizzled (Fz), Dishevelled, Van Gogh, and Prickle. Local propagation of polarity can occur accurately in the absence of a global cue, because PCP is sometimes propagated correctly across fat mutant clones on the order of 1 to 1.5 μm2. Ma et al. report that the propagation of polarity across fat mutant clones did not correlate strictly with the size or position of the clone, but rather it correlated with cell geometry, which was more likely to be disrupted in larger clones. PCP propagation was most disrupted in clones with the most variability in cell shape and, therefore, the most irregular packing. Genetically altering the shape of cells prevented PCP propagation, and a mathematical model suggested that the Fz-mediated PCP feedback loop was disrupted in cells with irregular geometry. The model also accurately predicted deviant polarity patterns within clones of irregularly shaped cells. Thus, in the absence of a global polarity signal, PCP can be propagated locally through the Fz feedback loop provided that cells are packed regularly. Cells in the wild-type wing epithelium are hexagonal in shape and uniform in size, but the mechanism by which this regular cell geometry influences the PCP has not yet been determined.